Solve for $x$ and $y$ using elimination. ${3x+2y = 15}$ ${-5x-2y = -17}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-2x = -2$ $\dfrac{-2x}{{-2}} = \dfrac{-2}{{-2}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {3x+2y = 15}\thinspace$ to find $y$ ${3}{(1)}{ + 2y = 15}$ $3+2y = 15$ $3{-3} + 2y = 15{-3}$ $2y = 12$ $\dfrac{2y}{{2}} = \dfrac{12}{{2}}$ ${y = 6}$ You can also plug ${x = 1}$ into $\thinspace {-5x-2y = -17}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ - 2y = -17}$ ${y = 6}$